Navy chiefs earlier warned the families of 18 sailors on board the submerged vessel to “prepare for the worst” after the two near-simultaneous explosions.
Antony offered “heartfelt condolences” to relatives of the dead.
It is not clear what caused the blasts. Sabotage has not been ruled out.
“A board of inquiry will cover the entire spectrum of the incident, we cannot rule out sabotage at this stage but all the indicators at this point do not support that theory,” navy chief Admiral DK Joshi said.
“Divers have opened the first hatch of the [submerged] submarine and are in the process of going down now. A detailed examination can only be carried out after the water is pumped out and the boat has come back to the surface.”
Earlier officials told the BBC they suspected the tragedy to be the result of an on-board error, not involving any outside agency.
Adm Joshi said that the boat has remained under water for much of Wednesday and that there had been no communication with the crew on board.
No bodies have yet been recovered.
Correspondents say that India has steadily developed its naval capabilities in recent years, motivated by its rivalry with neighboring China. But the country’s military has encountered numerous scandals and difficulties as it has done so.
On Tuesday the federal auditor suggested that the government may have paid too much for 12 helicopters from Anglo-Italian company AgustaWestland, saying procurement procedures designed to ensure value for money were not properly followed.
The blast on the INS Sindhurakshak took place after midnight (18:30 Tuesday GMT) and firefighters spent four hours putting out the blaze.
Officials said the diesel-powered vessel has been badly damaged.
One navy official told the BBC that “surviving an explosion of this huge scale” was rare.
Many sailors managed to jump to safety after the blast. Some were taken to hospital.
Dramatic images on Indian television showed a large fireball illuminating the sky. Smoke from the blaze could be seen in many parts of the city.
The authorities have offered assurances that there is no fear of any further explosions.
The Russian-built submarine was upgraded recently at a cost of $80 million (£52 million). At the time of the explosion it was said to be fully loaded with ammunition.
Russian firm Zvyozdochka, which refitted the submarine, said the vessel had been fully operational when it was returned to India in January. Reports from Russia say specialists are ready to help with the aftermath.
“It’s a great loss to us… it’s the greatest tragedy of recent times,” Antony told reporters in Delhi before leaving for Mumbai to visit the site of the incident.
The INS Sindhurakshak, which is powered by diesel and electricity, is one of the 10 Kilo-class submarines bought from Russia between 1986 and 2000. It is equipped with Russian Club-S cruise missile systems.
The submarine was sent to Russia for the refit in 2010 after a sailor on board was killed by a fire that broke out in the battery compartment while the submarine was docked at the Vishakhapatnam naval base in February that year.
Despite hours of searching the dark, muddy water inside a submarine crippled by twin explosions, Indian navy divers have yet to find the 18 sailors feared dead there, possibly because the heat of the blasts melted some hatches shut, the navy said Thursday.
There has been no word from the sailors — or even a knock on the submarine’s hull — since the explosions shot huge fireballs into the sky over a Mumbai navy base Wednesday morning.
“The trapped personnel have not been sighted nor recovered,” the navy said in a statement. It said round-the-clock diving efforts were being hampered by poor visibility inside the submarine.
“The heat of the explosion has melted parts of the internal hull, deforming the submarine hatches and preventing access to compartments,” the navy said.
“Eighteen brave sailors are feared to have lost their lives,” Prime Minister Manmohan Singh said in brief comments Thursday during a speech to mark the anniversary of India’s 1947 independence from Britain. “We pay homage to these brave hearts we have lost.”
The explosions in the submarine’s torpedo compartment sent nearby sailors jumping into the sea in panic and left the diesel-powered vessel partially submerged at a dock, with a portion visible above the waterline.
The navy statement said heavy duty pumps were being used to pump out water that flooded into the submarine after the explosions.
A navy official, speaking on condition of anonymity because he was not authorized to speak to the media, said there had been no contact with the sailors since the explosions, which lit up the sky above the base.
S.C.S. Bangara, a retired navy vice admiral, said there appeared to be little chance that any of the sailors could have survived.
“There would have been signs of life through tapping of the hull by the sailors, which is a known procedure for the rescue of sunken submarines,” he said.
Because the submarine was docked, navy watchmen were on the submarine rather than the normal crew, Admiral D.K. Joshi, the navy chief, told reporters Wednesday in Mumbai. At least some weaponry exploded in the near-simultaneous blasts, he added.
A video of the explosions filmed by bystanders showed an enormous ball of red and yellow fire rising hundreds of feet into the air.
Navy spokesman Narendra Vispute said the cause of the explosions was being investigated.
The 16-year-old Russian-made submarine, INS Sindhurakshak, was hit by an explosion in 2010 that killed one sailor and injured two others. The navy said that accident was caused by a faulty battery valve that leaked hydrogen, causing an explosion in the vessel’s battery compartment.
The sub recently returned from Russia after a 2½ year refit, overhaul and upgrade, said Rahul Bedi, an analyst for the independent Jane’s Information Group. Joshi, the navy chief, said it returned to India in April, and had been certified for use by the Indian navy.
Wednesday’s explosion comes just days after India’s navy launched its first home-built aircraft carrier, hailed by defense officials as a “crowning glory”.
Last year, India bought a Russian Nerpa nuclear submarine for its navy on a 10-year lease from Russia at the cost of nearly $1 billion, making it part of a select group of nations to operate nuclear-powered submarines.
India and Russia are long-time allies and Russia supplies about 70% of India’s military hardware.